Ok...
Oof, how to go about this...
I have two 6.5 gallon carboys, two 6 gallon carboys, and five of six 5 gallon carboys...
The 5 gallon carboy in that kit is certainly intended for secondary use, that is do the initial ferment in the bucket to accommodate the foaming, then once that is done put it in the glass carboy to finish.
The volume is measured to the shoulder of the carboy (I think) so there is more than 5 gallons allowed in the carboy.
Yeah, a 5 gallon might be too small if you want to do your primary ferment in, but hell, by the time you get that far where you are thinking about expanding beyond you will have sprung the $20 or whatever it is for a 6 gallon, you know?
I still regularly primary ferment in my plastic buckets. (There are three plastic fermenters in the house too, no wonder we don't have any storage space!)
Since I'm listing, I think I have 6 kegs too.

I stand by my recommendation. Midwest.
;)
There will be time for you to get the bug about how much more toys you want, or decide you don't want to do this at all, you are not out too much since you can resell your stuff.
Go with Midwest's or your local shop.

Well right now it's not a matter of getting bigger and better toys. I was just comparing and noticed that Midwest seems to be the only one doing the carboys is 5 gallon instead of 6. As long as 5 is 'good enough'. I'm not looking to expand, just want to make sure I'm all set from the start.

Using a 5 gal carboy as a primary will hurt you at some point. Here's a pic of my stout 3 days ago in the primary (a 6.5 gallon carboy!). There's a thing called a 'blow off' hose you can put on top of the carboy instead of the airlock to deal with this. It usually only happens when a) the carboy is too full (hence, using a larger vessel for primary when most of the fermentation is happening) or you have a really strong beer (high alcohol) or powerful yeast. Anyway, since this just happened to me (again) I figured I'd post it.

It seems whether or not a 5 gallon is big enough is dependent on how big of a batch I brew. Couldn't I just brew a little less volume? Or are these extract kits that I'd most likely be starting with set-up for 5 gallons?

yeah, cub, I wasn't trying to advise either way. I started with a 5 gallon (after the mr. beer kit) and never knew any different. 5 gallons is the 'standard' batch all the recipes and ingredients are made for. Go for it!!!!!!!!!!!!!!!!!!!

Is the basement a good place for fermenting or am I going to need more refrigerator space? I'm thinking the lagers need a fridge but not the ales.

The cold concrete floor is fine for your lagers in your area and fermenting in a dark place is good. Just use the big bucket for your primary ferment and put it in glass for the secondary for clarity and you are fine. If you plan on doing wine then 6 gal stuff is needed. Tony got me hooked and he gives good advise.

Everyone has hit the nail on the head just fine. 5 gallon glass for secondary, plastic for primary, since the plastic bucket is what? 6, 7 gallons marked, meaning you can fit extra room for the cap too.
The couple blow off's I had were from some insane wheat and re-using my yeast. Powerful combination. One blow off I had literally blew off the airlock cuz it got all plugged with crud, there was schlotz on the ceiling and in a nice circle around the carboy. Basement floor is great for lagers in the winter, but do some ales first to get your fix. Ales should take around 6 weeks, lagers should take at least three months.